Find the average value of the function LX TEX f (x) =4sin| on the interval [3,6]. COS 4

Q: Suppose that f satisfies the equation f(a +b) = f(a) + f(b) + a'b+ ab (E 1, b €R. Suppose further…

A: given :f(a+b)=f(a)+f(b)+a2b+ab2→(1)limx→0f(x)x=1 →(2)a.) put a=b=0 in…

Q: Find the exact length of the curve. x = 8 + 12t2 y = 3 + 8t3 Osts 3

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Q: Use the Laplace transform to solve the initial value problem y''+y'−2y=2e3t,y(0)=−1,y'(0)=4 y(t)=

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Q: A company produces x units of a product per month, where C(x) represents the total cost and R(x)…

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Q: Two polynomials P and D are given. Use either synthetic or long division to divide P(x) by D(X), and…

A: Topic = Algebra Px=Dx·Qx +RxPx=-x2+x-3+8x+1

Q: Test the series below for convergence using the Root Test. 8"n3n (7n +1)" n=1 The limit of the root…

A: Solution is given below

Q: Find the exact length of the polar curve. r = 0, 0 < 0 < 37/2 12.47776

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Q: Find the tangent lines. To the cubic y=x³-2x+3 parallel to the line 10x-y=3

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Q: Question 3 Algebraically compute f'(1) using the definition of the derivative, given that f (x) = x2…

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Q: Find an equation of the Hyperbola that has Foci (-1,–3) & (-1, 7) with asymptotes y = x+ & y = -a+…

A: Standerd equation of hyperboal is (x-h)2a2-(y-k)2b2=1where (h,k ) be the center

Q: Given the differential equation y' = 8y2 and y (0) = - 1 and its next few implicit derivatives y" =…

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Q: What are the angles of AABC with side lengths a = 12, b = 21, and c = 14? Round each angle to the…

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Q: For the series below calculate find the number of terms n that must be added in order the indicated…

A: The solution is given below

Q: Consider the DE У" - У" — бу %3D0 = e-2x and A) Verify that yı = 5, y2 y3 = ex are solutions of the…

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Q: 4.On which condition is the function differentiable at a point? A) continuous at the given point B)…

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Q: Substitute c = 2 in the formula for slope as follows. %3D + Ax) - g ( lim Ax- 0 m = Ax

A: We have to substitute in the slope formula.

Q: Given the equation y = 5 In| 6y | Find the Implicit derivative " dy/dx" of the function. You will…

A: We can find the derivative as below.

Q: Find k such that the line is tangent to the graph of the function. Function Line f(x) - kx y = Sx +…

A: The line is tangent to the given function then , there are two conditions :(1)  The function and the…

Q: Find the slope of the tangent line to the graph of the function at the given point. y = In x y 10…

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Q: repetitions.) P(x) = x - 4x2 - 19x 14 X = Write the polynomial in factored form. P(x) =

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Q: 1. (-1)*z* (2k)! for |피 < ® COS I = for |피 < 0 Use the power series representations for cos r and e-…

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Q: Espa Find an equation of the ellipse that has center (-5, 5), a minor axis of length 6, and a vertex…

A: Let's find.

Q: 2) Solve triangle ABC if a = 4,b=7,c 6. Round your answers to two decimal places.

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Q: III. Graph the following functions: 4. y lIn(x-3) 5. y= In(x-1) 6. y= In Vx-1

A: Consider the functions 4.   y=|ln(x-3)|5.   y=lnx-126.   y=lnx-1

Q: Find the derivative of y= e^x * sin(x) y= 5x^2 + cos(x) y= sec(x) + csc(x) y=…

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Q: Find term 4, term 6 and term 9 given by the formula: n2 + 2n + 1 a = ;n2 1. n+2 Determine whether…

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Q: 4+6 n i) The sequence { )is bounded by 6 n <ns ii) The 20 th. element of this sequence is

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Q: 2) (a) Using the method of Lagrange multipliers find the points at which e^(xyz) has a maximum or a…

A: Given problem:- (2) (a) Using the method of Lagrange multipliers find the points at which e^(xyz)…

Q: Use logarithmic differentiation to find dy/dx. (x + 1)(x - 7 (x - 1)(x + 7) x > 7 Step 1 The given…

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Q: Suppose that f(x) is a function with f(120) = 37 and f' (120) = 8. Estimate f(118.5). f(118.5) =

A: answer is in next step

Q: 1. lim cot x sinx X- x-nt cotx sinx

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Q: 2. Which phrase best describes a function which has the following table when it's graphed. -2 -1 2 7…

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Q: If the marginal cost function is given by c'(x) = 3x + 4x+ 3, then a general expression for the…

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Q: Use the simple interest formula to determine the missing value. p= $1475, r=?, t 2 years, i= $41.30…

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Q: Find the canonical prime factorization of the following using Fermat’s Method and solve for the…

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Q: 8. Differentiate. Use the correct notation to label your answer.n Joot ai bonIRanom at ogts viinolov…

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Q: Determine the location and value of the absolute extreme values of f on the given interval, if they…

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Q: The average value of the function y = 10 x In(4 x) on the interval [3,7] is О 50.05 O 152.14 O…

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Q: Consider the following. (If an answer does not exist, enter DNE.) h(x) = 5x3 - 3x5 %3D (a) Find the…

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Q: Exercise 1. Express the limit as a definite integral on the given interval a) lim T? cosxi Li=1' Ax,…

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Q: Find the quantities of each of the expressions below if u is (-5, 2) and v is -i+6j. Don't simplify…

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Q: Find the third derivative of the function. f(x) =  5 x

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Q: Find (f1)'(0). f(r) = | V1 + t2dt %3D (f1) (0) =

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Q: Complete the table. y = f(g(x)) U = g(x) y = f(u) 1. x +6

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Q: Find the net area and the area of the region bounded by y = 11 cos x and the x-axis between x= - and…

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Q: A rock is thrown upward from a bridge that is 53 feet above a road. The rock reaches its maximum…

A: Solved below

Q: The graph models the amount of radioactive element present over the course of a 10-minute…

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Q: Norman builds a rectangular pig pen with two parallel partitions using 150 meters of fencing…

A: let the length of Pig pen be "a"width be " b" Perimeter=150 metresPerimeter = 2(a+b)…

Q: — т3 + 3х2 — 2х — 1. + 3x2 %3D

A: answer is in next step

Q: Find the limit of the sequence an 14n+2 or 2+7n indicate that it is divergent. Select one: O…

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